ICTP Math Associates Seminar (Zoom Meeting) - Thursday 24 September at 14:00 (Vamsi Pritham Pingali)

[ICTP Math Section]

Math Associates Seminar


Thursday 24 September 2020, at 14:00, Central European Time


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Speaker: Vamsi Pritham Pingali (IISC,India)


Title: Numerical criteria for the solvability of generalised 
Monge-Ampere equations on projective manifolds


Abstract:
Generalised Monge-Ampere equations are a family of PDE that contain 
inverse Hessian equations like the J-equation, and special cases of the 
deformed Hermitian-Yang-Mills equation. I shall describe a couple of 
results about them. Firstly, these equations can be solved on projective 
manifolds if and only if Nakai-Moizeshon / Demailly-Paun-style 
intersection numbers are positive. This result improves a recent theorem 
of Gao Chen (who assumed uniform strict-positivity), and settles a 
conjecture of Lejmi-Szkelyhidi in the projective case. Secondly, 
assuming uniform strict-positivity, an equivariant version of the same 
result holds.
Thus, earlier results due to Collins-Szekelyhidi are recovered.
This work is joint with Ved Datar.